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Preventing competition using side payments: when
non-neutrality creates barriers to entry
Patrick Maillé, Bruno Tuffin
To cite this version:
Patrick Maillé, Bruno Tuffin. Preventing competition using side payments: when non-neutrality
creates barriers to entry. Netnomics, Springer Verlag, 2017, 18 (1), pp.3-22.
�10.1007/s11066-016-9110-6�. �hal-01398913�
(will be inserted by the editor)
Preventing Competition Using Side Payments: When
Non-Neutrality Creates Barriers to Entry
Patrick Maillé · Bruno Tuffin
the date of receipt and acceptance should be inserted later
Abstract Network neutrality is often advocated by content providers, stressing that side payments to Internet Service Providers would hinder innovation. However, we also observe some content provider actually paying those fees. This paper intends to explain such behaviors through economic modeling, illustrating how side payments can be a way for an incumbent content provider to prevent new competitors from entering the market. We investigate the conditions under which the incumbent can benefit from such a barrier-to-entry, and the consequences of that strategic behavior on the other actors: content providers, users, and the Internet Service Provider. We also describe how the Nash bargaining solution concept can be used to determine the side payment.
Keywords Network neutrality · Barrier to entry · Game theory
1 Introduction
The network neutrality debate is shaking up not only the telecommunication world but also governments, with laws passed worldwide. This vivid debate comes from In-ternet Service Providers (ISPs) complaining about some distant but heavy resource-consuming Content Providers (CPs) creating stress on their networks while not pay-ing anythpay-ing to them, because connected to the Internet through another ISP. The complainants therefore threat to block or slow down the traffic of those CPs if they
P. Maillé
Telecom Bretagne, 2 rue de la Châtaigneraie CS 17607, 35576 Cesson Sévigné Cedex, France Tel.: +33-2-99127028
Fax: +33-2-99127030
E-mail: patrick.maille@telecom-bretagne.eu B. Tuffin
Inria Rennes, Campus Universitaire de Beaulieu, 35042 Rennes Cedex, France Tel.: +33-2-99847494
Fax: +133-2-99847171 E-mail: bruno.tuffin@inria.fr
do not pay a side fee in order to participate to the network infrastructure mainte-nance and upgrade. This created a lot of protests from user associations and content providers claiming that it could harm innovation, freedom of speech, and the univer-sality of access principle among other issues. The issue is therefore basically whether the network should forbid such payments and other types of differentiation. For more information about the history of the network neutrality debate, and arguments from both sides, the reader is advised to go to [3,7,9,17] among the numerous publications on the topic.
Surprisingly, some big CPs, while officially strongly in favor of neutrality, are now giving side payments to ISPs. This is typically what Google (a major CP because of YouTube traffic) is doing, for instance in France with the main ISP Orange1, Netflix with Comcast and Verizon2, etc.
A question is then: what reason could drive big CPs to accept such side payments, when governments and user associations seem to fight on their side? In this paper, we investigate the relevance of a potential reason: accepting side payments when able to pay them could create a barrier to entry for potential competitors. Indeed, new entrants may incur initial costs and not have the same economies of scale as incumbents; therefore they may not be able to afford such payments. And from the incumbent perspective, the potential loss due to competitors entering the market may overcome the cost of side payments.
Note that some other interpretations for side payments have been proposed in the literature. Generally, side payments can be exchanged between actors to improve the coordination among them. They can be used in supply chains to improve their efficiency when several producers are involved [8]; or, closer to our problem, to avoid conflicts, an actor being paid for not participating in a later conflicting interaction [6, 15].
In the context of the net neutrality debate, and with the same interpretation of side payments as ours (from CPs to ISPs), a possible justification for such payments is that they can benefit both ISPs (receiving those payments) and CPs (although delivering them). This holds in situations where ISPs compete [2] and even when ISPs are mo-nopolistic and need side payments to invest more in infrastructure [10]. To the best of our knowledge, the present paper, along with its preliminary conference version [16], is the first contribution developing the idea of side payments’ use as a barrier to entry for CPs willing to enter the market and compete with incumbents.
The definition of barrier to entry has been a topic of discussion in the economic literature. It has first been defined by Bain in 1956 as “anything that allows incumbent firms to earn above-normal profits without the threat of entry" [1]. Other definitions followed; a historical development of definitions and a classification was provided in [12] with four different concepts of barrier to entry: i) an economic barrier to entry as a cost incurred by a new entrant but not by an incumbent, ii) an antitrust barrier to entry as a cost delaying entry and as a consequence reducing social welfare compared to an immediate cost, iii) a primary barrier to entry as a cost that constitutes a barrier to entry on its own, and iv) an ancillary barrier to entry as a cost that (indirectly)
1
http://www.theverge.com/2013/1/19/3894182/french- isp- orange- says- google- pays- to- send- traffic
reinforces other barriers to entry. A side payment falls into the third category (primary barrier to entry) since directly incurred by CPs and potentially preventing market entrance if benefits are not sufficient.
We propose in this paper to introduce and analyze a model describing a simple Internet supply chain with two content providers, end users, and ISPs as intermedi-aries. Demand from users will be assumed to depend on the access price at the ISP, and to follow a (traditional) linear form. We will analyze several scenarios:
– without side payment (a neutral network) and with competition between ISPs, – with side payments and competition,
– and with side payments and only the incumbent CP.
We will compare the outputs obtained in these scenarios. We will particularly look at revenues of CPs and the ISP, and consumer surplus. The goal is to get some insight about what strategy each actors should choose and whether or not some regulation rules should be imposed. If collusion between the incumbent CP and the ISP is ben-eficial, we will determine the side payment as a Nash bargaining solution [11], an axiomatic concept describing a solution of negotiation between players. Refinements of the model, considering uncertainties about the potential new entrant and the tem-poral aspects of its entry, are also investigated in this paper.
Note that modeling and analysis of barrier to entry in markets has of course been already studied, in a spirit somewhat similar to our work. A. Dixit in his seminal work [4] considers also a direct competition between an incumbent and an entrant providers, with linear demand too, but using a model less representative of the Inter-net, without ISPs as intermediaries while ISPs make important decisions here. [5] is another paper making use of a basic model, but working on a different issue: deter-mining the optimal number of firms in a market depending on fixed costs.
The rest of this paper is organized as follows. In Section 2, the mathematical model is presented, as well as the order of decisions among players, those playing first strategically anticipating the subsequent decisions of the others. Section 3 then provides the resulting values of revenues and consumer surplus in the three scenar-ios: no side payment, side payment but only the incumbent CP, and side payments with the two CPs. Those outputs are compared and conditions under which creating barriers to entry are beneficial for the incumbent provider are provided. Section 4 then describes how the incumbent CP and the ISP can negotiate the price, defined as the Nash bargaining solution. Two possible extensions of that model are then inves-tigated. In Section 5 we relax the assumption that the ISP-incumbent CP pair knows perfectly how the newcomer will perform (in terms of market shares, bandwidth us-age, and revenues): the reasoning is then based on expectations. Section 6 considers the temporal aspect, modeling the evolution of market shares after the possible en-trance of the competitor, and focusing on how long it would take that newcomer to cover its entry cost when side-payments are imposed or not. Finally, Section 7 con-cludes our paper and discusses extensions of the model.
2 Model
We consider the model presented in Figure 1. It describes a supply chain made of two content providers (CPs) in competition, end users, and one ISP as an intermediary. We just consider two CPs, believing that it is to provide some insight (which is the goal of the paper), but this can be generalized and will be the purpose of future work. To simplify the analysis, users are treated as a continuum, meaning that no user has individually an impact on the system (i.e., they are assumed infinitesimal). The total mass of base users is defined as Dmax.
Incumbent CP Entrant CP
ISP
No ISP
Set of end users
c c
p
Figure 1 Representation of relations between users, ISP and CPs
Figure 1 also shows the economic relations between actors: there is potentially a cost c (side payment) per unit of volume that CPs transfer to the ISP, and a sub-scription fee p per unit of customer paid by customers to the ISP. We also assume a revenue ri(respectively re) per unit of request for the incumbent CP (respectively
the entrant CP). Those revenues may for instance be due to advertisements displayed on the CP site and seen or clicked by customers, but could apply to other types of revenue (sales, subscriptions, etc.).
2.1 User demand
The subscriber demand (mass of users subscribing to the ISP) D is assumed to be linear in price, of the form
D = (Dmax− αp)+
where α is the price sensitivity parameter and (·)+= max(·, 0). This type of model
is traditional in economics [11] and has often been used in models studying barriers to entry such as [4].
We define from total demand D the mass Diof requests at the incumbent and the
mass Deof users making use of the new entrant service. Without loss of generality
the request unit of mass is chosen such that in the case where the incumbent is alone, we have Di = D. In that situation, we also have De = 0. On the other hand when
both propose their services, Di = γiD and De = γeD with γi, γe > 0 being the
proportion of requests at each CP. Typically, we will consider that the arrival of the new entrant results in a loss of traffic for the incumbent (hence γi < 1), due to less
subscribers or connections, but also that γi+ γe ≥ 1, meaning that users might use
both services (there is no exclusivity) when both CPs are present. In other words, the total traffic increases upon the new entrant arrival, due to a more attractive catalog, while traffic for the incumbent decreases because in part moved to the new entrant.
Note here that demand does not depend on content, more exactly on whether the two CPs are present or not. This can be justified by the fact that the CPs we are considering are just a part of the Internet content, and having one or two substitutable CPs does not limit the user range of activities (or has a negligible impact).
A metric of interest as a measure of consumer satisfaction from the users’ side is Consumer Surplus (S), which is defined as the aggregated difference between the maximum prices consumers are willing to pay and the prices actually paid. Graphi-cally, it is the hashed area in Figure 2.
p 0 Dmax D = Dmax− αp demand D
Figure 2 Consumer surplus with a linear demand.
2.2 Internet Service Provider
The ISP is characterized by its revenue
R = pD + cvi+ cve
where
– the other terms correspond to the side payments: viand veare the total volume of
requests for each CP, with
vi= βiDi and ve= βeDe
with βiand βethe (average, per time unit) units of volume consumed per request
to each CP;
2.3 Content Provider Revenues
Recall that we have defined Di and Deas the masses of requests of the incumbent
and new entrant CPs respectively, and riand rethe respective revenues generated per
(mass unit of) request.
The revenues of the incumbent and entrant CPs are then respectively: Ri= riDi− cvi = (ri− βic)Di
Re= (re− βec)De.
2.4 Order of decisions
CPs, ISP and users have to make strategical decisions, but they are not all made at the same time scale. The decisions are as follows:
1. First, the ISP and incumbent CP decide (through a negotiation) the side payment; 2. Then the ISP decides the subscription price p;
3. Finally users adapt their demand to the proposed services and price.
Decisions are made strategically: actors playing first make their decision anticipating the subsequent decisions of the others. Hence those decisions can be analysed using the backward induction method [14].
This model is studied in the next section in the case of three scenarios: 1. no side payments and both CPs in the market;
2. side payments and only the incumbent provider; 3. side payments and both CPs.
The interest of considering those three scenarios, and comparing them, is manyfold: First, it will help the incumbent provider to decide whether or not to be in favor of side payments and their level of magnitude, by comparing the revenues to the cases where the new entrant is there. Second, it helps the ISP to decide a strategy on side payments by looking at its revenue, and also if negotiating with the incumbent is beneficial as opposed to the threat of network neutrality regulation. Finally, the same comparison is helpful for regulatory bodies to investigate if it harms competition and consumer surplus.
Note that in all cases, the subscription price is chosen to maximize the ISP rev-enue
where we set γe= 0 and γi= 1 if the incumbent is alone. To simplify the notations,
define
C := c(βiγi+ βeγe)
as the average side payment per (unit of) user. From R = (p + C)(Dmax− αp), we
get
p = Dmax 2α −
C 2 as the price maximizing the ISP revenue.
Note that this price could be negative if C > Dmax/α but this would mean a
demand larger than the base Dmax. Taking p = 0 is then optimal.
3 Outputs for given side payments
This section describes the outputs for the three scenarios and then deduces the strate-gic decisions of players.
3.1 Without side payments
When no side payments are applied, i.e., c = 0, we can use our previous derivations (optimal price, corresponding demand value) to get new expressions for revenues and consumer surplus. This yields
p = Dmax 2α D = Dmax 2 Ri= riγi Dmax 2 Re= reγe Dmax 2 R = Dmax 2 4α S = Z Dmaxα Dmax 2α (Dmax− αp)dp = Dmax2 8α .
3.2 With side payments but only the incumbent content provider
When the incumbent provider is in a monopolistic position, and is charged side pay-ments by the ISP, then our model still applies, with γi = 1, γe = 0, and C = cβi.
For a given side payment c, we get, following the same substitution procedure as in the previous subsection,
p =Dmax 2α − cβi 2 (assumed non-negative) D = Di = Dmax 2 + α cβi 2 Ri = (ri− βic) Dmax 2 + α cβi 2 R = 1 4α(Dmax+ αcβi) 2 S = Z Dmaxα Dmax 2α − cβi 2 (Dmax− αp)dp =Dmax 2 + 2Dmaxcβiα + c2β2iα2 8α .
3.3 With side payments and the two content providers The case of two CPs and side payments yields
p = Dmax 2α − c(βiγi+ βeγe) 2 D = Dmax 2 + α c(βiγi+ βeγe) 2 Ri= γi(ri− cβi) Dmax 2 + α c(βiγi+ βeγe) 2 Re= γe(re− cβe) Dmax 2 + α c(βiγi+ βeγe) 2 R = 1 4α(Dmax+ αc(βiγi+ βeγe)) 2 S = Dmax 2+ 2D maxc(βiγi+ βeγe)α + c(βiγi+ βeγe)2α2 8α .
3.4 Comparison and resulting strategic decisions
We can make several remarks when comparing the outputs for the three scenarios: 1. First, the new entrant will not enter the market if its revenue is negative, i.e., if
c > re/βe. The incumbent CP, if wishing to prevent the new entrant to reach
customers, must agree on side payments of at least that amount. Clearly also, the incumbent cannot accept a non-negative revenue, hence we must have c ≤ ri/βi.
It implicitly means that the revenue per unit of data ri/βihas to be larger for the
incumbent than that re/βeof the new entrant. This will be assumed from now
2. But in order for the incumbent to be in favor of side payments, and therefore to create a barrier to entry, its revenue (when alone) has also to be larger than when there is no side payments. It happens when (ri−βic)(Dmax+αcβi) > riγiDmax,
i.e., if c is in the interval
−(Dmax− αri) −qβ2
i(Dmax− αri)2+ 4αβi2ri(1 − γi)Dmax 2αβ2
i
,
−(Dmax− αri) +qβ2
i(Dmax− αri)2+ 4αβi2ri(1 − γi)Dmax 2αβ2
i
.
The left bound of the interval being negative, we actually just need c to be smaller than the right bound.
Note that the incumbent can at the same time pay a level of fee to ensure that the new entrant will not be there and ask for no side payments publicly. This is typically what would happen if the revenue with side payment and barrier to entry is i) larger than that with the new entrant (and still a side payment), but ii) smaller than that with a “neutral" ISP. It corresponds to the situation when the CP would prefer the neutral situation, but being unsure that it will be applied, goes to the best of two evils. It may also be a strategical behavior even if monopoly plus side payments is the best option, in terms of image and in order to better negotiate the level of payments (see next section). It may explain what Google is doing in France: paying a side payment to the major ISP (Orange), but asking for a neutral network.
3. The ISP has also to agree that the level of side payment increases its revenue R. This is always the case with respect to a neutral situation. But, in general, a single CP will be preferred if csβi> c2(βiγi+βeγe) where csis the side payment when
there is only one CP (through a corresponding negotiation), and c2when there are
two. To look at a sufficient condition with simplified notations, when cs= c2, we
just need βi> βiγi+ βeγe. But this inequality is true if the incumbent induces a
large amount of traffic (typically what Google does with YouTube).
4. Consider now consumer surplus. If a regulator investigates the consequences of side payments, they are actually beneficial from a customer point of view. This comes from the fact that due to side payments, the ISP can reduce the access price, hence higher levels of demand and satisfaction from end users. This situation is actually at the expense of CPs.
Example 1 Figure 3 displays the revenues in terms of c when Dmax = 10, α = 1,
βi = 0.7, βe = 2, ri = 6, re = 3, γi = 0.7, and γe = 0.5 (arbitrary values).
We display the revenues Ri and R in the competitive case when c < re/βe, and
in the monopolistic case when re/βe ≤ c < ri/βi. We clearly see the threshold at
re/βe = 1.5 where the new CP strategy changes from entering the market to not
entering it. We also see that the incumbent CP is better off with a side payment when above but close to that threshold.
Table 1 presents some numerical computations for the three scenarios, for two values of c. If the price is c = 0.5, the incumbent CP even gets a higher revenue than in the two other cases when alone, but with such a c, the new entrant would be
0 2 4 6 8 0 20 40 60 c re v enues R Ri Re
Figure 3 Revenues of the ISP (R), the incumbent CP (Ri), and the new entrant CP (Re), in terms of the
side payment c.
Table 1 Some numerical values for the three scenarios for two values of c
c Scenario p D Ri Re R S
— No side payment 5 5 21 7.5 25 12.5
0.5 Monopoly 4.825 5.175 29.23875 — 26.780625 13.3903125
0.5 Side payment and competition 4.6275 5.3725 21.2482375 5.3725 28.86375625 14.43187812
2 Monopoly 4.3 5.7 26.22 — 32.49 16.245
2 Side payment and competition 3.51 6.49 20.8978 -3.245 42.1201 21.06005
present; we would be in the situation of side payment and competition. On the other hand, we see that with a price c = 2 the new entrant should not enter the market, and the incumbent gets a higher revenue than without side payment or with a side payment smaller than re/βe= 1.5 (something clear on Figure 3). The revenue of the
ISP is also higher than without side payments, hence c = 2 benefits both the ISP and incumbent CP with respect to a neutral situation, hence an incentive to cooperate. In terms of consumer surplus, the higher the side payment, the better it is.
4 Side payments negotiation
In the previous section, we were discussing the optimal strategies when the side pay-ment was fixed. The purpose of this section is to investigate how those paypay-ments can be defined, if they are eventually authorized by regulators. Actually several possibili-ties exist. A first one would be that the price be chosen by the ISP trying to maximize its revenue. It is clear from the revenue expressions that it would be set at a level such that the CP revenue is becoming 0, at the same time increasing demand because most ISP revenue is then paid by the CP. In such a case, there would be a strong opposition and lobbying from CPs, and the risk of neutrality regulation would be very large.
We consider here the situation where there is a negotiation between the incumbent CP and the ISP about the side payment. The solution of this negotiation is assumed to
be the result of an axiomatic model called Nash bargaining solution [14]. Placed into our context, the ISP and incumbent CP independently choose a set of acceptable side payments, the ones providing a non-negative revenue in the interval (re/βe, ri/βi)
ensuring for the incumbent to impose barriers to entry. If there is no agreement, a threat is executed: due to possible complaints related to the network neutrality de-bate, the threat is no side payment, c = 0. Since this negotiation may end up with several equilibria, the most likely to be played is the one maximizing the product of the utilities minus the utility at the threat [13]. In other words, that equilibrium side payment c maximizes
K := (Ri(c) − Ri(0))(R(c) − R(0)),
where Ri(c) and R(c) are the revenues with side payment c, and that maximizer is
called the Nash bargaining solution.
Since c > re/βe, only the incumbent CP is present and
K = (ri− βic) Dmax 2 + α cβi 2 − riγi Dmax 2 cβi 4 (cαβi+ 2Dmax) .
We can differentiate this term with respect to c and get optimum values (that will be summarized to solving polynoms in c of degree three). Instead of providing this analytic list which does not bring much insight, we illustrate on our running example the Nash bargaining solution for c.
Example 2 Figure 4 displays K in terms of c (still when Dmax = 10, α = 1, βi =
0.7, βe = 2, ri = 6, re = 3, γi = 0.7, and γe = 0.5). One can check that, with
1.5 2 2.5 3 30 35 40 c K Figure 4 K in terms of c.
our parameters, K is maximized at c = 2.137012. Table 2 presents the output at this value. The incumbent CP revenue is not maximized (because smaller than when c = 2), but much larger than when there is no side payment. The same applies for the ISP. It is indeed a compromise on which they both agree.
We also display in Figure 5 the evolution of that Nash bargaining c in terms of the proportion of requests βithat the incumbent still attracts when the new entrant is
Table 2 Numerical values for c as the Nash bargaining solution. c Scenario p D Ri Re R S 2.137012 Nash Bargaining 4.2520458 5.7479542 25.88931223 — 33.03897748 16.51948874 0 1 2 3 4 0 re/βe 5 10 βi c
Figure 5 Nash bargaining c in terms of βi.
present, all other parameters being defined as before. This side payment c is larger than the threshold re/βe = 1.5 for “small" values of βi, and sticks to that threshold
as soon as βi≥ 1.0.
5 Anticipating a potential competitor
Our previous analysis was assuming that the parameters related to a new entrant were known. It would work if side payments were decided when the competitor enters the market (and assuming all parameters could again be derived quickly). Though, the side payments are not likely to be that reactive to the market: (i) it would be too visible that they are barriers to entry, and (ii) negotiations would take time.
We assume here that the new entrant parameters are unknown, but that there is a common knowledge about the distribution of the parameters of a potential new entrant. The goals of the incumbent and the ISP are then to maximize their respective expectedrevenues.
More specifically, we consider that the parameters riand βiare fixed and known,
but that there is a joint density function f (·) on parameters re, βe, γe, γi. Depending
on the random values, for a fixed c
– if re− cβe≥ 0, the competitor enters the market and we get the values Ri(c) and
R(c) computed in Subsection 3.3;
– if re− cβe< 0, the competitor does not enter the market and we get the values
From this, we can easily (numerically) compute the expected revenues for the incum-bent E[Ri(c)] =R Ri(c)f (re, βe, γe, γi)dredβedγedγi, new entrant E[Re(c)], and
ISP E[R(c)].
The price c can be negotiated between the ISP and the incumbent CP trying to maximize their expected revenue. Again as in the previous section, the Nash bargain-ing solution c maximizes
K = (E[Ri(c)] − E[Ri(0)])(E[R(c)] − E[R(0)]).
Deriving theoretical formulas seems intractable, but we are able to obtain nu-merical results about expected revenues in terms of c and then about the negotiation between the ISP and the incumbent CP.
Example 3 Assume as in our previous example that Dmax= 10, α = 1, βi= 0.7 and
ri= 6. We also assume that βe, reand γeare uniformly distributed over respectively
[βi/2, 2βi], [0, 1.2ri] and [0.7, 1], and that γi = 1.1 − γe. Figure 6 displays the
expected revenues in terms of c. The revenue of the new entrant decreases with c,
0 2 4 6 0 20 40 c re v enues R Ri Re
Figure 6 Expected revenues in terms of c.
while that of the ISP increases. For the incumbent CP on the other hand, there is a maximum. Due to the randomization, there is no discontinuity, in contrast to Figure 3. Figure 7 displays the value of K in terms of c. when using the expected revenues. It is maximized close to c = 4.6. Even if the revenue of the ISP keeps increasing with c, there is an interest to trade off with the incumbent CP, hence a Nash bargaining solution that is finite, and larger than the price maximizing the incumbent CP revenue.
6 Adding temporality to the model
In the previous sections, we have considered that the new entrant would attract a pro-portion γeof the demand (and incurs a loss of a proportion 1 − γiin the incumbent’s
requests), and studied the values of the side payment for which the new entrant is deterred from playing in the market.
0 2 4 6 0 50 100 c K K
Figure 7 K in terms of c in the expected case.
But we did not enter the details of what happens over time when the newcomer CP enters the market. Indeed, it is not reasonable to assume that a proportion γeof
the total demand (i.e., requests) goes to the new entrant immediately after it entered, while a proportion 1 − γi immediately stops using the services of the incumbent
CP. Instead, we can reasonably expect that users progressively adopt the new entrant (while some also progressively leave the incumbent), and γeand γithen correspond
to the stationary proportions of users for each CP, i.e., after convergence of the adop-tion process. The reasoning in the previous secadop-tions was therefore for that staadop-tionary situation. In particular, the barrier to entry intended to ensure that the new entrant would not make benefits in that situation. However, if we consider the dynamic set-ting, lower values of the side payments may be enough to prevent the newcomer from entering the market: that newcomer could indeed make benefit in the long run, but would have to face losses over a significant amount of time. Depending on how long the newcomer can “survive” without making benefits, and the maximum amount of debt it can accumulate, this may be sufficient to discourage it from entering the game. We study this time aspect in the present section. More specifically, considering that the newcomer enters the market at time 0, the proportion γi(t) (resp., γe(t)) of
requests choosing the incumbent (resp., the newcomer) CP is assumed of the form γi(t) = γi+ (1 − γi)e−ωt
γe(t) = γe− γee−ωt,
where the parameter ω represents the speed at which the changes in user behavior occur. The digital market being very volatile, reasonable values for ω are of the order of 1/2 per year, meaning that a CP can lose as much as 40% of its demand within one year if it performs badly (here, if γi= 0).
As expected, at t = 0 the new entrant has no customers (γe(0) = 0) and all
re-quests go to the incumbent (γi(0) = 1), and the long-term proportions of the previous
Note that if no newcomer CP enters the market, we are already at the stationary situation and nothing changes over time, hence we are at the situation analyzed in Subsection 3.2.
To carry out the temporal analysis, we consider a discount factor δ, so that one monetary unit in t years is worth e−δtmonetary units of today. And over a time period spanning from 0 to T , an actor with revenue per time unit U (t) at time t is sensitive to the average discounted revenue
¯ U (T ) := δ 1 − e−δT Z T t=0 U (t)e−δtdt.
Similarly, we will denote by ¯R(T ), ¯Ri(T ), and ¯Re(T ) the average discounted
rev-enue of the ISP, the incumbent CP, and the newcomer CP, respectively, with the time horizon T .
In all generality, we should allow the price p and the side-payment level c to vary over time. But we think it is more realistic to consider them fixed since users are likely to be reluctant to frequent price changes, and side-payments are decided through negotiations and contracts, and are difficult to change. At most one change in those values is considered here, at time 0 when those strategic decisions are made. As a result, the total user demand D = [Dmax− αp]+will be constant over time.
6.1 No newcomer entrance
Assume that the newcomer does not enter the market; then γi(t) = 1 for all t, and
recalling the results from Subsection 3.2 we have constant values for all revenues. Hence for any T we have
¯ Ri(T ) = (ri− βic) Dmax 2 + α cβi 2 ¯ R(T ) = 1 4α(Dmax+ αcβi) 2 , and the other values of interest are
p =Dmax 2α − cβi 2 (assumed non-negative) D = Di = Dmax 2 + α cβi 2 S = Dmax 2 + 2Dmaxcβiα + c2β2iα 2 8α .
6.2 Arrival of the newcomer
Assuming that the side-payment level c is chosen before the ISP price p, and follow-ing the classical backward induction method, we analyze how p should be set when c is fixed.
6.2.1 ISP revenue-maximizing price
For given values of c and p, the ISP revenue at time t is R(t) = Dp + Dc(βiγi(t) + βeγe(t)).
Therefore, the average revenue at the horizon T is ¯ R(T ) = Dp + Dc(βiγi+ βeγe) + +Dcβi(1 − γi) − βeγe 1 − e−δT δ Z T t=0 e−(ω+δ)tdt = Dp + DC + D ˜C δ ω + δ 1 − e−(ω+δ)T 1 − e−δT
where C := c(βiγi+ βeγe) as previously, and ˜C := c(βi(1 − γi) − βeγe) = cβi− C.
When T is fixed, we can define the constant
C0 := C + ˜C δ ω + δ
1 − e−(ω+δ)T
1 − e−δT ,
so that the revenue of the ISP is ¯
R(T ) = D × (p + C0), and as in Section 3 the revenue-optimizing price is
p = Dmax 2α − C0 2 , assumed positive, leading to ¯ R(T ) = 1 4α(Dmax+ αC 0)2 .
Note that C0 > C, so (for a given side-payment level) the price set here is below the one we obtained when ignoring the transient phase and focusing only on the limit case (what we did in Section 3). In the numerical examples shown later on, we will consider that the ISP has a very large horizon T , so that C0= C + ˜Cω+δδ .
Now, let us express the revenues of both CPs as functions of the side-payment c.
6.2.2 Revenue for the incumbent CP
At time t, the incumbent CP gets revenue per time unit (ri− βic)γi(t)D, so over a
time horizon Ti, its average discounted revenue is
¯ Ri(Ti) = (ri− βic)D γi+ (1 − γi) δ ω + δ 1 − e−(ω+δ)Ti 1 − e−δTi ,
with D = Dmax− αp =Dmax+C 0 2 .
6.2.3 Revenue for the newcomer CP
Similarly, at time t the newcomer CP gets (if it enters the market) a revenue per time unit Re(t) = (re− βec)γe(t)D. But entering the market also involves a fixed cost
(investments in the new service and/or in infrastructure or licensing) which we denote by Ee. That fixed cost had no impact when focusing on the long-term revenue only
as in Section 3, but here with a finite horizon Teor a nonzero discount rate δ, the
question for the new entrant becomes: will the aggregated discounted revenues in the first Tetime units (say, years) be enough to cover the entry investment Ee?
Our model allows to answer that question: the aggregated discounted revenues for the newcomer between times 0 and Tecan indeed be expressed as
Z Te t=0 e−δtRe(t)dt = (re− βec)Dγe 1 − e−δTe δ − 1 − e−(ω+δ)Te ω + δ . (1) As a result, if the newcomer can sustain being nonprofitable for a duration at most Te, then it will enter the market if and only if
(re− βec)Dγe 1 − e−δTe δ − 1 − e−(ω+δ)Te ω + δ > Ee. (2) Dmax α βi βe ri re γi γe δ ω Ee Ti Te 10 1 0.7 2 6 3 0.7 0.5 0.04 0.5 20 10 10
Table 3 The parameters used for the numerical analysis
With respect to Section 3, having the side payment be such that re − βec <
0 is sufficient, but not necessary anymore to prevent the newcomer from entering. Figure 8 shows the aggregated revenue of (1) when the time horizon Tevaries and
the other parameters are given in Table 3: while Section 3 suggests a minimum side payment of re/βe= 1.5, the figure shows that lower values can be sufficient to deter
the newcomer from entering the market, especially if it has a short time horizon: in a neutral network (c = 0) the newcomer would make benefits in less than five years, while it would take more than ten years with c = 1.
This effect, and the dependence on the fixed entry cost Ee, is further illustrated
on Figure 9 showing how long it takes for the newcomer to cover that fixed cost with the revenues obtained from entering the market and attracting users. When there is no fixed cost (Ee= 0), we find again that the newcomer does not enter the market if
c > re/βe = 1.5, and makes immediate benefits otherwise. But with a fixed cost to
enter the market, even side payments below re/βesignificantly harden the work for
the newcomer, delaying by several years the time to rentability.
6.3 When can the ISP-incumbent CP pair create a barrier to entry?
As before, a barrier-to-entry side payment can be agreed upon between the ISP and the incumbent CP when the three conditions below are met.
0 2 4 6 8 10 0
Ee
Newcomer time horizon Te
Aggre g ated re v enue c = 0 c = 0.5 c = 1 c = 1.5 c = 2
Figure 8 Cumulated discounted revenue over an horizon Tefor the newcomer CP and comparison with
its fixed cost Ee. The ISP computes its price based on an infinite time horizon (T = ∞).
0 0.5 1 1.5 0 5 10 15 20 c T ime before rentability (years) Ee= 0 Ee= 5 Ee= 10 Ee= 15 Ee= 20
Figure 9 Time for the newcomer CP to cover its fixed cost Eedepending on the side payment c. The ISP
computes its price based on an infinite time horizon (T = ∞).
1. The newcomer is effectively deterred from entering the market, i.e., (2) is satis-fied.
2. The CP prefers paying the side payment (and being alone) than having to face the competitor in a neutral network. In the former case, as seen in Subsection 6.1 the average discounted revenue ¯Ri(Ti) is (ri− βic)
Dmax 2 + α cβi 2 , while in the latter case (taking c = 0 in (1)) it equals
Dmaxri 2 γi+ (1 − γi) δ ω + δ 1 − e−(ω+δ)Ti 1 − e−δTi .
Defining ¯γi:= γi+ (1 − γi)ω+δδ 1−e −(ω+δ)Ti
1−e−δTi , this amounts as in Section 3 to
c ≤ −(Dmax− αri) + q β2 i(Dmax− αri)2+ 4αβ2iri(1 − ¯γi)Dmax 2αβ2 i .
3. And the ISP also prefers this situation to the neutral (and competitive) one, i.e., 1 4α(Dmax+ αcβi) 2 ≥ 1 4αDmax 2 , which is always the case.
Summarizing, one has the conditions on the parameters for having the possibility of a barrier-to-entry side payment that benefits both the ISP and the incumbent CP. As an example, we display on Figure 10 the values of the parameters γi, γesuch that
those conditions are met (the domain below the curve for a given Te), when the other
parameter values are those given in Table 3. The figure illustrates that, at least for our parameters, a barrier to entry is very likely to occur: only when the incumbent performs very well (i.e., maintains a large market share γiwhen the newcomer enters
the market), such a barrier to entry may be undoable, because the incumbent is not too harmed by competition. Also, when the new entrant has a short time horizon (needs to rapidly cover its entry costs) then, as expected, it is more vulnerable to barriers to entry.
0 0.2 0.4 0.6 0.8 1
0 0.5 1
Long-term incumbent market share γi
Long-term ne wcomer mark et share γe Te= 2 Te= 10
Figure 10 Below the curves, a barrier-to-entry is feasible and benefits both the incumbent CP and the ISP.
7 Conclusions
In this paper, we have introduced a simple model representing the Internet supply chain, and analyzed the relevance for incumbent CPs to agree to pay side payments (depending on parameter values) to ISPs in order to introduce a barrier to entry for
competitors. This helps to understand the current behavior of some big CPs, paying those fees despite militating against non-neutral networks. We believe that even if simple, the presented model provides some insight on the consequences on all cate-gories of actors.
Our main contribution is the development of a model and analysis tools to under-stand such phenomena. Our illustrations are based on arbitrarily-chosen numerical values. An important next step is to carry out econometric studies to fit those pa-rameters to some specific cases. Such an approach was not possible here because of the secrecy around commercial agreements among actors in the Internet. But with access to those data, one can directly apply our method to be able to anticipate the impact of side payments on newcomer entries and the (possible) optimal side pay-ment level. For example, the model can be used by an incumbent content provider wishing to avoid the arrival of a new competitor, or by a regulator (with access to CP-ISP commercial agreements) to determine whether competition is hindered and an intervention is necessary.
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